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What would be the particuler solution guess for the inhomogeneous ODE

  1. Feb 12, 2013 #1
    Inthis article, the authors present the inhomogeneous equation

    $$\ddot{\phi}_2 + \phi_2 + g_2\phi_1^2 + \omega_1\ddot{\phi}_1 = 0,\tag{11}$$

    where

    $$ \phi_1 = p_1 \cos(\tau + \alpha), \tag{13}$$

    The original solution of the inhomogeneous equation is:

    $$\phi_2 = p_2\cos(\tau + \alpha) + q_2\sin(\tau + \alpha) + \frac{g_2}{6}p_1^2[\cos(2\tau + 2\alpha) - 3] $$
    $$+ \frac{\omega_1}{4}p_1[2\tau\sin(\tau + \alpha) + \cos(\tau + \alpha)]. \tag{14}$$

    but I got
    \begin{align}
    \phi_2 = p_2 \cos(\tau + \alpha) + q_2 \sin(\tau + \alpha) + \frac{g_2p_1^2}{6} [\cos(2(\tau + \alpha)) -3]+ \omega_1p_1cos(\tau+\alpha)
    \end{align}

    I got the solution by guessing the particular solution **\begin{align}
    \phi_2 = p_2 \cos(\tau + \alpha) + q_2 \sin(\tau + \alpha) + C \cos(2(\tau + \alpha)) + D\sin(2(\tau + \alpha)) + E.
    \end{align}**


    Where is my mistake?
     
  2. jcsd
  3. Feb 12, 2013 #2

    haruspex

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    Re: what would be the particuler solution guess for the inhomogeneous

    Have you checked whether your solution satisfies the original equation?
     
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